Hi Jos,
You would probably want to consult with a BK attorney. The BK would need to include all debts including those they wish to reaffirm. It is my understanding that if they (you) continue to pay the payments then they have reaffirmed the debt and this loan is no longer included in the BK. I am NOT a BK attorney but that is my understanding.
If you stop paying the mortgage the lender can foreclose on the property. There would be no “stay” to be lifted unless the payments were not current and a foreclosure had been started.
Keep in mind that there is an acceleration clause in most standard form Deeds of Trust that allows the lender to call the note due and payable if there has been a transfer of the beneficial interest of the property. Whenever you purchase a property “subject to” you are taking the risk that this lender will no longer accept installment payments and the entire balance will become due. The filing of the BK may alert the lender to the fact that the transfer took place.